From an in-universe point of view, why hasn’t Katara, Tenzin, Bumi, or Kya considered communicating with their dad’s spirit through Korra, or vice versa? As of book 1, she had finally connected to her spiritual side and Aang’s spirit had manifested before her. Past Avatars have also been known to be able to posses the body of the current Avatar.
Because Aang is dead
This is a subtle distinction, but it seems that the "previous lives" scenes aren't fully-fledged conversations with fully-conscious individuals. That is, Avatar Aang can appear to Korra to convey wisdom or experience, but we never see them just "chatting," the way she does with Iroh in the spirit world. Iroh is still living a life, making friends, discovering new things, and behaving like a living, thinking person when Korra meets him. By contrast, the previous Avatars seem to only exist as advisors to the current Avatar, and seem devoid of any life (or even existence) between moments when the current Avatar needs them.
Every "past life conversation" we see onscreen follows the same structure: the current Avatar has a problem, and the past Avatar provides a story from their life to help illustrate a possible solution. If the franchise continues this may be contradicted, but so far the signs seem to indicate that the previous Avatars don't "live on" in the sense of having the ability to continue forming opinions and having experiences, but rather that they're more like a conscience or intuition, giving guidance when the Avatar needs it, based on what each incarnation learned and experienced during their life.
If this is the case, Aang's spirit wouldn't be able to "converse" with Katara through Korra at all, even if she tried. Aang is dead, and all that remains are his memories and his wisdom, which pass to his successor and are experienced as conversations.
Korra is also has a lot of issues with the spiritual side of her calling so it is difficult enough for her To contact aang, also by all accounts aang led a full happy life and his family had time to accept his passing and move on , also it would have bogged down the show with another story line it didn't need
According to the Avatar Wiki, Korra lost connection with her past lives during Harmonic Convergence. She had the ability to communicate with past avatars for only a short time.